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Unformatted text preview: Math 114, Lecture 1 Final Exam May 9, 2004 YOUR NAME: _________________ CIRCLE YOUR TA’s NAME: Mr. Ye Fang Ms. Shantala Mukherjee Do all eight problems. Each problem or part is worth the indicated number of points. There are 150 points altogether. Do not spend too much time on any one problem. There are eleven printed
pages in this exam, including this cover page. ' Page Possible points Your score
Page 2 12
Page 3 12
Page 4 14
Page 5 20
Page 6 20
Page 7 16
Page 8 16
Page 9 16
Page 10 12
Page 11 12 TOTAL 150 3 Problem 2 (12 points) Solve AABC' if a = 3, b = 4, and 7 = If necessary, leave your answers in terms of the values of trigonometric or inverse trigonometric functions. Problem 4 Let 6 = (2, 3) and 5: (—1, 5).
(a) (5 points) Find the vector 6 + 5, and ﬁnd its length. (b) (5 points) Find the vector 26 — 35, and ﬁnd its length. (c) (5 points) What is the value of (25 — 35)  (ii + (d) (5 points) Find the angle between the vector 25 —— 33 and the vector 6 + If necessary,
leave your answer in terms of the value of trigonometric or inverse trigonometric functions. . . . 1
Problem 6 Suppose that x is an angle in the second quadrant With cos(a:) = ——. Suppose also 3
1
that y is an angle with sin(y) = —Z and tan(y) > 0. (a) (5 points) Find sin(x) and cos(y). (b) (6 points) Find sin($ + y) and cos(:c + y). (c) (5 points) In which quadrant is the angle at + y? Problem 7 continued:
(c) (8 points) 2:3 — 3302 + 7:10 —~ 5 = 0. (d) (8 points) 0052(m) — sin2(:c)  3 cos(x) = 1. Problem 8 continued: (b) (12 points) Sketch the graph of y = f(2:c) + 3: 11 ...
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This note was uploaded on 08/08/2008 for the course MATH 114 taught by Professor Nanciu during the Fall '07 term at Wisconsin.
 Fall '07
 NANCIU
 Algebra, Trigonometry

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